Payback Period
Meaning of Payback
→ Payback period measures the amount of time required for a business to recover the initial cost of an investment from the cash inflows generated by the investment.
→ It answers the question:
“How long will it take to get our original investment back?”
→ Payback is particularly useful when a business is concerned about cash flow and risk.
Calculation of Payback
When annual cash inflows are equal:
Payback period = Initial investment ÷ Annual cash inflow
Example — Equal Cash Inflows
A business invests $100,000 in new machinery.
Annual cash inflow = $25,000
Payback = $100,000 ÷ $25,000
= 4 years
→ The initial investment will be recovered after 4 years.
When Cash Inflows Are Unequal
→ Add the annual cash inflows cumulatively until the original investment has been recovered.
Example:
| Year | Cash inflow | Cumulative cash inflow |
|---|---|---|
| 1 | $30,000 | $30,000 |
| 2 | $35,000 | $65,000 |
| 3 | $40,000 | $105,000 |
| 4 | $45,000 | $150,000 |
Initial investment = $100,000
→ At the end of Year 2, $65,000 has been recovered.
→ Amount still to recover:
$100,000 − $65,000 = $35,000
→ Year 3 provides $40,000.
Fraction of Year 3 = $35,000 ÷ $40,000 = 0.875
Therefore:
Payback = 2.875 years
≈ 2 years 11 months
Interpretation of Payback
→ Shorter payback period → investment recovers its initial cost sooner → generally lower exposure to long-term uncertainty.
→ Longer payback period → investment takes longer to recover its cost → greater exposure to changes in demand, costs and other risks.
→ If a business has a maximum acceptable payback period, an investment can be compared with this target.
Advantages of Payback
→ Simple and easy to calculate.
→ Easy for managers to understand.
→ Focuses on cash flow.
→ Useful when liquidity is important.
→ Highlights how quickly the initial investment is recovered.
→ Useful where technology may become outdated quickly.
Limitations of Payback
→ Ignores cash flows after the payback period.
→ Does not directly measure total profitability.
→ Does not consider the time value of money.
→ A project with a quick payback may generate lower total returns than a project with a longer payback.
Accounting Rate of Return (ARR)
Meaning of ARR
→ Accounting Rate of Return (ARR) measures the average annual profit from an investment as a percentage of the average investment.
→ Unlike payback, ARR focuses on accounting profit rather than the time taken to recover the initial investment.
Formula
ARR = (Average profit ÷ Average investment) × 100
→ This is the formula to use for the Cambridge calculation.
Calculating Average Profit
Average profit = Total profit over the investment period ÷ Number of years
→ If profit figures are given for each year, add them together and divide by the number of years.
Calculating Average Investment
→ Where the investment has a residual value:
Average investment = (Initial investment + Residual value) ÷ 2
→ If there is no residual value:
Average investment = Initial investment ÷ 2
Example
A business invests $100,000 in machinery.
The expected annual profits are:
| Year | Profit |
|---|---|
| 1 | $15,000 |
| 2 | $20,000 |
| 3 | $25,000 |
| 4 | $30,000 |
Residual value = $0
Step 1: Calculate total profit
$15,000 + $20,000 + $25,000 + $30,000
= $90,000
Step 2: Calculate average profit
$90,000 ÷ 4
= $22,500
Step 3: Calculate average investment
($100,000 + $0) ÷ 2
= $50,000
Step 4: Calculate ARR
ARR = ($22,500 ÷ $50,000) × 100
= 45%
→ The investment generates an average annual accounting return of 45% on the average investment.
Interpretation of ARR
→ Higher ARR → investment generates a higher average accounting return relative to the average amount invested.
→ Lower ARR → investment generates a lower average accounting return.
→ A business can compare the ARR with:
- another investment
- a target ARR
- the return from alternative investments
- the cost of finance.
→ If a business has a target ARR of 30% and a project has an ARR of 45%, the project exceeds the target.
Advantages of ARR
→ Uses profit, which is important when assessing profitability.
→ Considers profits over the whole investment period, unlike payback.
→ Easy to calculate and understand.
→ Expressed as a percentage, making comparisons easier.
Limitations of ARR
→ Uses accounting profit rather than cash flow.
→ Does not consider the time value of money.
→ Average profit can hide differences between individual years.
→ The result depends on accounting measures such as depreciation.
→ Does not show how quickly the initial investment is recovered.
Payback vs ARR
| Payback | ARR |
|---|---|
| Measures time taken to recover investment | Measures average annual profit as a % of average investment |
| Focuses on cash inflows | Focuses on accounting profit |
| Answer expressed in years/months | Answer expressed as a percentage |
| Shorter payback generally preferred | Higher ARR generally preferred |
| Useful for assessing liquidity and recovery time | Useful for assessing profitability |
| Ignores returns after payback | Considers profits throughout the investment period |
| Does not consider time value of money | Does not consider time value of money |
Exam Application
→ If the question asks “How quickly will the investment be recovered?” → use Payback.
→ If the question asks “What average percentage return does the investment generate?” → use ARR.
→ When comparing two projects:
Project with shorter payback → recovers the investment sooner.
Project with higher ARR → generates a higher average accounting return.
→ These methods may give different indications. Therefore, managers should also consider risk, cash flow, strategic objectives, availability of finance and other factors before making the final investment decision.